equity portfolio

suppose you have Standard & Poor 500, and a portfolio to hedge. The portfolio does not eactly mirror the index. We then use B (beta).

I always studied beta as a measure of the sensitivity of the portfolio to mkt movements, but the definitin provided by th book is this one:

" Beta is the slope of the best-fit line obtained when excess return on the portfolio over the risk-free rate is regresses against the excess return of the mkt over the risk-free rate"

which I do not really get. What does "regressed" mean?

does this simply mean that beta= covariance/variance starting from the assumption of a linear affine relation that the excess return for a certain stock is equal to the excess return for the mkt plus an error?

I am trying to be as clear as possible but the confusion in my mind does not guarantee a great result...

Beta

You are correct - the Beta is a measure of the sensitivity of the stock relative to the index.

The beta is basically solved by carrying out linear regression i.e. beta is the gradient of the fitted straight line of the plot of the market returns (above risk free) vs individual stock returns (above risk free). Using beta= covariance/variance is perfectly fine.